Backward Euler Method
An example of an implicit method is the backward Euler method:
![$\displaystyle \underline{\hat{x}}(n) \isdefs \underline{\hat{x}}(n-1) + T\dot{\...
...nderline{\hat{x}}(n-1) + Tf[n,\underline{\hat{x}}(n),\underline{u}(n)] \protect$](http://www.dsprelated.com/josimages_new/pasp/img1702.png){kind=small}
Because the derivative is now evaluated at time
instead of 
,
the backward Euler method is implicit. Notice, however, that if time
were reversed, it would become explicit; in other words, backward
Euler is implicit in forward time and explicit in reverse time.
Next Section:
Trapezoidal Rule
Previous Section:
Forward Euler Method
